PNNL-26790

Prepared for the U.S. Department of Energy under Contract DE-AC05-76RL01830

Effect of Silicon in U-10Mo Alloy August 2017

EJ Kautz A Devaraj L Kovarik CA Lavender VV Joshi

PNNL-26790

Effect of Silicon in U-10Mo Alloy EJ Kautz A Devaraj L Kovarik CA Lavender VV Joshi August 2017 Prepared for the U.S. Department of Energy under Contract DE-AC05-76RL01830 Pacific Northwest National Laboratory Richland, Washington 99352

iii

Purpose and Scope

The purpose of this document is to provide a method for evaluating the effect of silicon (Si) impurity content on U-10Mo alloys. Si concentration in U-10Mo alloys has been shown to impact the following: volume fraction of precipitate phases, effective density of the final alloy, and 235U enrichment in the γ-UMo matrix. This report presents a model for calculating these quantities as a function of Si concentration, which along with fuel foil characterization data, will serve as a reference for quality control of the U-10Mo final alloy Si content. Additionally, detailed characterization using scanning electron microscope imaging, transmission electron microscope diffraction, and atom probe tomography analysis showed that Si impurities present in U-10Mo alloys form a Si-rich precipitate phase, U2Si2MoC. This newly discovered Si-rich phase is introduced in this document, as it significantly impacts how Si content affects final alloy microstructure and properties.

v

Acronyms and Abbreviations

APT atom probe tomography BCC body-centered cubic C carbon EDS energy dispersive spectroscopy FA final alloy FFC Fuel Fabrication Capability HEU highly enriched uranium LEU low-enriched uranium Mo molybdenum SEM scanning electron microscopy Si silicon U uranium U-10Mo uranium alloyed with 10 weight percent molybdenum UC uranium carbide UMo body-centered cubic γ-uranium-molybdenum alloy 235U enrichment weight of 235U as a percentage of total weight of U

vii

Contents

Purpose and Scope ....................................................................................................................................... iii Acronyms and Abbreviations ....................................................................................................................... v 1.0 Introduction .......................................................................................................................................... 1 2.0 Silicon Balance Model for Calculating Effective Density and Enrichment of the Final Alloy ............ 2

2.1 Motivation for Silicon Balance Model Development .................................................................. 2 2.2 Si Balance Model Background ..................................................................................................... 3

2.2.1 Overview ........................................................................................................................... 3 2.2.2 Assumptions ...................................................................................................................... 4

2.3 Step 1: Estimating the Number of U, Mo, C, and Si Atoms in UMo, UC, and U2Si2MoC Phase in the FA, per the FA Composition Specifications ...................................................................... 4

2.4 Step 2: 235U Enrichment in γ-UMo Matrix as a Function of Si Concentration ............................. 5 2.5 Step 3: Estimating Densities of UMo Matrix, UC, and U2Si2MoC Phases ................................. 7

2.5.1 UMo Matrix....................................................................................................................... 7 2.5.2 U2Si2MoC ......................................................................................................................... 7 2.5.3 UC ..................................................................................................................................... 8

2.6 Step 4: Estimating the Volume Fractions of UMo, UC, and U2Si2MoC ..................................... 8 2.7 Step 5: Estimating the Effective Density of the Final Alloy ........................................................ 9

3.0 Future Work ........................................................................................................................................ 13 4.0 References .......................................................................................................................................... 13

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Figures

1 Overall SEM Backscattered Electron Image of As-Cast and Homogenized U-10Mo Alloy Showing All Precipitates ...................................................................................................................................... 2

2 Unit Cell of the U2Si2MoC Phase ........................................................................................................ 3 3 Enrichment of 235U wt% in UMo Matrix of FA vs. Si Concentration, Assuming Two Different

Cases ..................................................................................................................................................... 6 4 Volume Percentages of U2Si2MoC and UC vs. Silicon Concentration in Final U-10Mo Alloy .......... 9 5 Effective Density of Final Alloy Based on Rule of Mixtures as a Function of Si Concentration from

0 to 1000 ppm ..................................................................................................................................... 10 6 Mo Concentration (in at%) in UMo Matrix as a Function of Si Concentration for Both Cases 1

and 2. ................................................................................................................................................... 11 7 Mo Concentration (in wt%) in UMo Matrix as a Function of Si Concentration for Cases 1 and 2. ... 12

1

1.0 Introduction

The U.S. Department of Energy, National Nuclear Security Administration’s Office of Material Management and Minimization is developing monolithic metallic fuel to meet the objectives of the United States High Performance Research Reactor Program (USHPRR). The metallic fuel selected to replace current dispersed high-enriched uranium (HEU) fuels is a low-enriched uranium (LEU) 10-weight-percent (wt%) molybdenum alloy with less than 20 wt% 235U. The Fuel Fabrication (FF) pillar of the USHPRR has undertaken a series of activities in order to develop a fabrication process that will yield qualified fuel. A number of activities have been conducted in order to increase understanding of the effect of processing conditions on the final formed fuel microstructure. A variety of factors can directly affect the final U-Mo LEU alloy performance, including chemistry of raw materials (e.g., HEU plus a depleted U-Mo master alloy), the casting process (e.g., melting procedure, melt-mold and melt-gas interactions), and the thermomechanical processes used in fuel fabrication (e.g., hot and cold rolling, annealing). It has been determined that the final U-10Mo alloy microstructure (e.g. degree of phase transformation) and properties are influenced by amounts of impurities and the secondary phases that they form, such as uranium carbides (UC), U2Si2MoC, and oxides These impurity and second-phase particles not only alter the transformation kinetics and may also form second phase particles with not only 238U but also 235U thus scavenging the matrix from 235U.

In work reported in a recent publication (Jana et. al 2017), it was observed that Si enrichment along γ-UMo grain boundaries is responsible for early onset of the phase transformation observed during sub-eutectoid annealing. Based on prior chemical analysis of UMo samples (Nyberg et. al 2015), Si is known to be an impurity element present in U-10Mo alloys. It is hypothesized that the UC and U2Si2MoC phases may be present in the HEU feedstock or could be formed during the melting and casting stages in U-Mo alloy preparation. Depending on when the UC and U2Si2MoC phases are formed, the 235U enrichment in these secondary phases and the U-Mo matrix can vary. Enrichment of the U-Mo matrix can also depend on the volume fraction of U2Si2MoC, which is in turn dependent on the Si concentration. Therefore, investigating the effect of varying Si content (in ppm) on the U-10Mo system is essential to better understanding how impurity content impacts phase transformation kinetics as a function of thermomechanical processing parameters. A model that can accurately predict final fuel microstructure and properties as a function of Si concentration is needed.

Prior work presented in Devaraj et al. (2016a) determined the effect of carbon concentration on the density of the final formed fuel. In this 2016 report, it was hypothesized that 235U could either remain in the γ-UMo matrix or form UC, thereby affecting final fuel microstructure, properties, and performance. A similar concept was adopted for development of the model presented here, in which different assumptions regarding scavenging of 235U are investigated.

The model presented in this work was developed to in order to estimate the following as a function of Si concentration: U2Si2MoC and UC volume fractions, effective density of the final U-10Mo alloy, and 235U enrichment in the U-Mo matrix.

This report is organized in the following manner: Section 2 presents the silicon balance model, including motivation and background, relevant equations, and results. Future Work is presented in Section 3, and all references cited are provided in Section 4.

2

2.0 Silicon Balance Model for Calculating Effective Density and Enrichment of the Final Alloy

2.1 Motivation for Silicon Balance Model Development

Based on detailed microstructure characterization results by scanning electron microscopy – energy dispersive spectroscopy (SEM-EDS), transmission electron microscopy (TEM), and atom probe tomography (APT) (Devaraj et al. 2016b), the as-cast and homogenized U-10Mo final alloy (FA) received from the Y-12 National Security Complex typically contains two impurity phases: uranium carbide (UC) and a Si-rich phase, U2Si2MoC. The newly discovered (U2Si2MoC) phase has a tetragonal lattice, and the γ-UMo matrix has the body-centered cubic (BCC) structure. Hereafter, the γ-UMo matrix phase will be referred to as the UMo phase (Burkes et al. 2009, 2010; Joshi et al. 2015a, 2015b). Based on backscattered electron SEM images, the UMo phase appears light gray, whereas UC appears dark gray and U2Si2MoC appears black, as shown in Figure 1, below.

Figure 1. (a) Overall SEM Backscattered Electron Image of As-Cast and Homogenized U-10Mo Alloy Showing

All Precipitates¶. (b–d) Coexisting UC precipitates (gray contrast) and U2Si2MoC precipitates (darker contrast). (e) Independent U2Si2MoC precipitates. (f) EDS spectrum from U2Si2MoC precipitate. (g) SEM-EDS mapping of a UC precipitate with U2Si2MoC precipitates around it. (h) Si map (red color) of the same structure shown in (g).

TEM analysis revealed the crystal structure of the newly discovered U2Si2MoC phase in the FA, which has not yet been reported in literature. The structure of this new phase as deducted from TEM and APT and verified with computational studies is shown in Figure 2, with corresponding space group and lattice parameters.

3

Lattice Parameters:

a = 6.68 Å

c = 4.32 Å

Space Group: P4mbm

Figure 2. Unit Cell of the U2Si2MoC Phase¶. Per unit cell there are 4 U atoms (gray), 4 Si atoms (blue), 2 Mo atoms (purple), and 2 C atoms (black). Lattice parameters (a, c) and space group are indicated adjacent to the unit cell schematic.

The presence of U2Si2MoC in the FA has implications for properties of the FA due to its influence on mechanical processing and transformation kinetics. The presence of the U2Si2MoC phase directly affects final fuel microstructure; therefore it is important to be able to predict U2Si2MoC volume fraction as a function of Si concentration, where Si is a known impurity element in the FA. No model predicting volume fraction of a Si-rich phase as a function of Si concentration has been reported in literature; thus, a model was developed that links volume fraction of U2Si2MoC in the FA to Si concentration (from 0–500 ppm). This model, referred to as the “Si balance model” is presented here.

2.2 Si Balance Model Background

2.2.1 Overview

The goal of the Si balance model is to calculate the following as a function of Si concentration from 0–500 ppm:

1. 235U enrichment in γ-UMo matrix

2. volume percentages of UC and U2Si2MoC phases

3. effective density of the FA

4. Mo concentration in the γ-UMo matrix.

All of the quantities listed above are presented as plots in this report in order to observe trends in these quantities with increasing Si concentration.

In order to calculate the above quantities, the following major steps were completed; they are subsequently detailed in this report (with all calculations provided in the accompanying Excel worksheet, named “Si_balance_calculations_June2017):

1. Step 1: Estimate the number of 235U, 238U, Mo, C, and Si atoms in the UMo matrix, UC phase, and U2Si2MoC phase in the FA, per FA composition specifications.

2. Step 2: Estimate 235U enrichment in γ-UMo matrix as a function of Si concentration.

4

3. Step 3: Estimate densities of UMo matrix, UC phase, and U2Si2MoC phase.

4. Step 4: Estimate the volume fraction of UMo matrix, UC phase, and U2Si2MoC phase.

5. Step 5: Estimate the effective density of the FA.

2.2.2 Assumptions

All calculations were done for 1000 g of FA, and the following assumptions were made:

1. FA composition is U89.9−yMo10C0.1Siy, with 19.75 wt% of total U as 235U (19.75 wt% enrichment). Based on the FA composition listed here, we are assuming the amounts of Mo and C are fixed, whereas the amounts of Si and U in the FA vary.

2. The solubility of C in the UMo matrix is zero.

3. C is partitioned between UC and U2Si2MoC phases. Carbon in the FA is used to form U2Si2MoC first, with the remaining C in UC. The UC volume fraction varies with Si concentration in the FA.

4. All the C atoms in the FA form UC, where C concentration is fixed at 1000 ppm (1 g out of the total 1000 g alloy mass).

5. The solubility of Si in the UMo matrix is zero. All Si in the FA is in the U2Si2MoC phase.

6. Two different bounding assumptions are made for where 235U is located in the FA. These assumptions were made in order to obtain lower and upper bounds of enrichment in the γ-UMo matrix. These two assumptions, referred to as Case 1 and Case 2, respectively, are described below:

a. Case 1: All U in UC and U2Si2MoC phases is 235U. All remaining 235U in FA is in the UMo matrix.

b. Case 2: All U in UC and U2Si2MoC is 238U. All 235U is in UMo matrix.

7. UMo matrix density is calculated based on the mass and volume per unit cell of the γ-UMo BCC structure.

a. Mass per unit cell is calculated by multiplying the atomic percentages of 235U, 238U, and Mo atoms by the 2 atoms per unit cell.

b. The volume of a single unit cell is calculated from the theoretical unit cell parameter, a, assuming the hard sphere model.

8. The UMo matrix density varies with 235U enrichment; thus, because of Assumption 6, the matrix density varies as a function of Si concentration. UMo matrix density is not assumed to be constant, as was previously assumed in Devaraj et al. (2016a).

6. Based on the above assumptions, the mass of each element in 1000 g of FA was estimated for a range of Si concentrations from 0 to 500 ppm. The concentration of Si expected in the FA is up to 500 ppm.

2.3 Step 1: Estimating the Number of U, Mo, C, and Si Atoms in UMo, UC, and U2Si2MoC Phase in the FA, per the FA Composition Specifications

The total number of atoms of 235U, 238U, Mo, C, and Si in the FA was calculated for different values of Si concentration from 0–500 ppm, given the mass of the element (in grams), Avogadro’s number (atoms/mol), and atomic mass (grams/mol), as seen in Equation 1.

5

In many equations included in this report, units are listed in brackets next to the corresponding parameter.

𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑜𝑜𝑜𝑜 an 𝑁𝑁𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑒𝑒𝑎𝑎 =𝑤𝑤𝑁𝑁𝑤𝑤𝑤𝑤ℎ𝑎𝑎 𝑜𝑜𝑜𝑜 𝑁𝑁𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑒𝑒𝑎𝑎 [𝑤𝑤] × 6.023𝑥𝑥1023[𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎𝑁𝑁𝑜𝑜𝑒𝑒 ]

𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑤𝑤𝑎𝑎 𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎 [ 𝑤𝑤𝑁𝑁𝑜𝑜𝑒𝑒]

(1)

Next, the number of atoms per phase was calculated for UMo, UC, and U2Si2MoC.

In order to estimate the number of atoms per phase, the distribution of U, Mo, C, and Si was considered.

C partitioning between the Si-rich phase (U2Si2MoC) and UC is accounted for in this model by assuming C is first allocated to the Si-rich phase, and then all remaining C in the FA (per FA composition specifications) is in the UC phase. We also assume all Si in the FA is in U2Si2MoC, and then calculate the number of Si atoms in this phase. Then we calculate the number of C atoms in U2Si2MoC by dividing the total number of Si atoms in this phase by 2 (since the ratio of C:Si atoms is 1:2). C content in the FA is constant, so all remaining C is assumed to be in UC. The total number of atoms in each phase was calculated based on the number of Si atoms for Si concentrations varying from 0 to 500 ppm. The basic equations used to calculate total number of atoms in each phase are provided in Equations 2–4, below:

𝑇𝑇𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒 𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈𝑈𝑈𝑜𝑜 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁= [#𝑈𝑈 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝐹𝐹𝐹𝐹 − (#𝑈𝑈 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈𝑈𝑈 + #𝑈𝑈 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈)]+ (#𝑈𝑈𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝐹𝐹𝐹𝐹 − #𝑈𝑈𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈)

(2)

𝑇𝑇𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒 𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈𝑈𝑈 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁 = (#𝑈𝑈 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝐹𝐹𝐹𝐹 − #𝑈𝑈 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈) ∗ 2 (3)

𝑇𝑇𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒 𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁

= (2 ∗ 𝑇𝑇𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒 𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑆𝑆𝑤𝑤 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎) + (2 ∗12∗ 𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑆𝑆𝑤𝑤 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎)

(4)

2.4 Step 2: 235U Enrichment in γ-UMo Matrix as a Function of Si Concentration

As previously reported in Devaraj et al. (2016a), the fuel specification nominally requires a 19.75 wt% enrichment of 235U in the FA, the bulk of which comes from the HEU feedstock. The UC and U2Si2MoC phases may be present in the HEU feedstock, or they could be formed during the melting and casting stages in the UMo alloy preparation. Depending on when the UC and U2Si2MoC phases are formed, the 235U enrichment in these secondary phases and the UMo matrix can vary. The enrichment of the UMo matrix can also depend on the volume fraction of U2Si2MoC, which is in turn dependent on the Si concentration.

Here, the enrichment of 235U in the UMo matrix is calculated for two limiting cases, as previously presented in the Assumptions section (2.2.2) of this report (and listed below for clarity):

Case1: All uranium in UC and U2Si2MoC is 235U.

Case 2: All uranium in UC and U2Si2MoC is 238U.

Case 1 and Case 2 are assumed to be two extremes; the actual matrix enrichment is expected to fall in between the enrichment values calculated for these two assumptions.

Enrichment of the UMo matrix is plotted for Case 1 and Case 2 in Figure 3, below:

6

Figure 3. Enrichment of 235U wt% in UMo Matrix of FA vs. Si Concentration, Assuming Two Different Cases¶:

(Case 1) All Uranium in UC and U2Si2MoC is 235U, and (Case 2) All Uranium in UC and U2Si2MoC is 238U.

Enrichment of the UMo matrix is lower in Case 1 than in Case 2 because in Case 1, the U in the UC and U2Si2MoC phases is assumed to be 235U, which means there is less 235U in the UMo matrix, resulting in a lower enrichment. As Si concentration increases, matrix enrichment decreases in Case 1 and increases in Case 2, which again occurs due to the initial assumptions of where 235U is allocated in the FA. In Case 1, since all U in UC and U2Si2MoC is assumed to be 235U, as Si concentration increases, there are more Si atoms in the U2Si2MoC phase, and thus there are more 235U atoms in this phase, and fewer in the UMo matrix, which results in decreasing enrichment with increasing Si concentration. For Case 2, since no 235U is in the UC and U2Si2MoC phases, as Si concentration increases, more 238U is allocated to UC and U2Si2MoC, leaving a higher enrichment of 235U in the UMo matrix.

7

2.5 Step 3: Estimating Densities of UMo Matrix, UC, and U2Si2MoC Phases

Next, densities of each phase were calculated for Case 1 and Case 2. Different densities were calculated for each case because the molecular weights of 238U and 235U are different, and although there may be the same number of U atoms per unit cell in each phase, the density will vary based on number of 235U or 238U atoms per unit cell. Additionally, the density of the UMo matrix was calculated as a function of Si concentration, because the enrichment varies with increasing Si concentration.

2.5.1 UMo Matrix

In order to calculate density of the γ-UMo matrix, weight percentages of 235U, 238U, and Mo in the matrix were converted to atomic percentages. Next, the total mass per unit cell was calculated, and finally, density was calculated given the total mass per unit cell and the volume per unit cell. Equations 5–7 (below) were used in the matrix density calculation. The same approach was applied for both Case 1 and Case 2.

𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎 𝛾𝛾𝑈𝑈𝑈𝑈𝑜𝑜 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑎𝑎𝑁𝑁3] = 𝑎𝑎03 (5)

𝑈𝑈𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝛾𝛾𝑈𝑈𝑈𝑈𝑜𝑜 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒

= �𝑎𝑎𝑎𝑎% 𝑈𝑈235

100∗

2 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒

∗𝑈𝑈235𝑤𝑤𝑁𝑁𝑜𝑜𝑒𝑒

∗𝑁𝑁𝑜𝑜𝑒𝑒

6.02223 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎�

+ �𝑎𝑎𝑎𝑎% 𝑈𝑈238

100∗

2 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒

∗𝑈𝑈238𝑤𝑤𝑁𝑁𝑜𝑜𝑒𝑒

∗𝑁𝑁𝑜𝑜𝑒𝑒

6.02223 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎�

+ �𝑎𝑎𝑎𝑎% 𝑈𝑈𝑜𝑜

100∗

2 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒

∗𝑈𝑈𝑜𝑜 𝑤𝑤𝑁𝑁𝑜𝑜𝑒𝑒

∗𝑁𝑁𝑜𝑜𝑒𝑒

6.02223 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎�

(6)

𝐷𝐷𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈𝑜𝑜 𝑈𝑈𝑎𝑎𝑎𝑎𝑁𝑁𝑤𝑤𝑥𝑥 =𝑎𝑎𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒 𝑤𝑤𝑁𝑁𝑎𝑎𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝛾𝛾𝑈𝑈𝑈𝑈𝑜𝑜 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑤𝑤]𝑣𝑣𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎 𝛾𝛾𝑈𝑈𝑈𝑈𝑜𝑜 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑎𝑎𝑁𝑁3]

(7)

UMo matrix density varies with Si concentration from 17.283 to 17.288 g/cm3 for Case 1, and 17.275to 17.284 g/cm3 for Case 2. It is noted here that the effective density of the γ-UMo matrix with 19.75 wt% 235U was previously calculated to be 17.33 g/cm3 (constant) as is detailed in Devaraj et al. (2016a). The UMo matrix density calculated in this report is generally in agreement with that which was previously calculated; however, in this work, we account for variation of the matrix density with 235U enrichment, which is the reason for the small variation in calculated density values between the 2016 report and this work.

2.5.2 U2Si2MoC

U2Si2MoC has a tetragonal lattice with 12 atoms per unit cell (4 U atoms, 4 Si atoms, 2 Mo atoms, and 2 C atoms).

To estimate the mass of a unit cell of U2Si2MoC, the masses of 4 U atoms, 4 Si atoms, 2 Mo atoms, and 2 C atoms are added, as shown below in Equation 7, where the U molecular weight variable here is either 238.0285 g/mol for 238U or 235.04 for 235U.

From the lattice parameters of U2Si2MoC (a = 6.68 Å, c = 4.32 Å), the volume of a unit cell is calculated using Equation 8 and then used to estimate the density of U2Si2MoC using Equations 9–10:

8

𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑎𝑎𝑁𝑁3] = 𝑎𝑎2 ∗ 𝑎𝑎 (8)

𝑈𝑈𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑤𝑤]

=4 atoms

unit cell × [U molecular weight gmol]

6.023 × 1023 atoms/mol+

4 atomsunit cell × 28.0855 g/mol6.023 × 1023 atoms/mol

+2 atoms

unit cell × 95.96 g/mol6.023 × 1023 atoms/mol

+2 atoms

unit cell × 12.011 g/mol6.023 × 1023 atoms/mol

(9)

𝐷𝐷𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 [𝑤𝑤𝑎𝑎𝑁𝑁3] =

𝑈𝑈𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒

(10)

The two densities calculated for the U2Si2MoC phase for Case 1 and Case 2 are 10.93 g/cm3 and 11.03 g/cm3, respectively.

2.5.3 UC

Similar to the density calculations performed for the U2Si2MoC phase, UC density was calculated by first calculating the volume of the unit cell, given lattice parameter (a), and the mass of the unit cell. Volume, mass, and density were calculated using Equations 11–13, below:

𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑈𝑈𝑈𝑈 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑎𝑎𝑁𝑁3] = 𝑎𝑎3 (11)

𝑈𝑈𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑈𝑈𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒 [𝑤𝑤] =4 atoms

unit cell × [U molecular weight gmol]

6.023 × 1023 atoms/mol+

4 atomsunit cell × 12.011 g/mol

6.023 × 1023 atoms/mol (12)

𝐷𝐷𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈 [𝑤𝑤𝑎𝑎𝑁𝑁3] =

𝑈𝑈𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑈𝑈𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈 𝑁𝑁𝑒𝑒𝑤𝑤𝑎𝑎 𝑎𝑎𝑁𝑁𝑒𝑒𝑒𝑒

(13)

The two densities calculated for Case 1 and Case 2 are 13.44 g/cm3 and 13.60 g/cm3, respectively. The density of 235UC was estimated to be 13.4394 g/cm3 in Devaraj et al. (2016a), which is consistent with calculations reported here.

2.6 Step 4: Estimating the Volume Fractions of UMo, UC, and U2Si2MoC

The volume fraction of each phase was calculated, given the total number of atoms per phase, volume per atom in each phase, and the total volume of all phases in the FA, as shown in Equation 14:

𝑣𝑣𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑤𝑤𝑜𝑜𝑒𝑒 𝑜𝑜𝑜𝑜 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁 =𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁𝑎𝑎 𝑤𝑤𝑒𝑒 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁 ∗ 𝑣𝑣𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑝𝑝𝑁𝑁𝑁𝑁 𝑎𝑎𝑎𝑎𝑜𝑜𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁

𝑎𝑎𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒 𝑣𝑣𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑎𝑎𝑒𝑒𝑒𝑒 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁𝑎𝑎 (14)

In order to understand how the volume fractions of the Si-rich phase and UC vary with increasing Si concentration, the volume percentages (volume fraction multiplied by 100) of these phases were plotted versus Si concentration from 0 to 500 ppm (Figure 4).

9

Figure 4. Volume Percentages of U2Si2MoC and UC vs. Silicon Concentration in Final U-10Mo Alloy

As Si concentration increases, the volume percent of U2Si2MoC increases, because all Si in the FA is in this phase. Because C content is fixed, the UC volume percent must decrease, since as Si concentration increases, more C is needed to form this Si-rich phase, meaning less C is available to form UC.

2.7 Step 5: Estimating the Effective Density of the Final Alloy

Here, effective density of the FA was calculated as a function of Si concentration for Case 1 and Case 2.

By using the calculated individual phase densities of each of the phases (detailed above in Step 3), and the volume fraction of each phase, the effective density of the FA was estimated by the rule of mixtures, provided below in Equation 15:

𝐸𝐸𝑜𝑜𝑜𝑜𝑁𝑁𝑎𝑎𝑎𝑎𝑤𝑤𝑣𝑣𝑁𝑁 𝑑𝑑𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑜𝑜𝑤𝑤𝑒𝑒𝑎𝑎𝑒𝑒 𝑎𝑎𝑒𝑒𝑒𝑒𝑜𝑜𝐷𝐷

= (𝐷𝐷𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈 × 𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑤𝑤𝑜𝑜𝑒𝑒 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈)

+ (𝐷𝐷𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈𝑜𝑜 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁 × 𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑤𝑤𝑜𝑜𝑒𝑒 𝑜𝑜𝑜𝑜 𝛾𝛾𝑈𝑈𝑈𝑈𝑜𝑜 )

(15)

10

+ (𝐷𝐷𝑁𝑁𝑒𝑒𝑎𝑎𝑤𝑤𝑎𝑎𝐷𝐷 𝑜𝑜𝑜𝑜 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈 𝑝𝑝ℎ𝑎𝑎𝑎𝑎𝑁𝑁 × 𝑉𝑉𝑜𝑜𝑒𝑒𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑤𝑤𝑜𝑜𝑒𝑒 𝑜𝑜𝑜𝑜 𝑈𝑈2𝑆𝑆𝑤𝑤2𝑈𝑈𝑜𝑜𝑈𝑈)

The variation in density as a function of silicon concentration is given in Figure 5 for the two cases considered to estimate the upper and lower bound for FA density.

Figure 5. Effective Density of Final Alloy Based on Rule of Mixtures as a Function of Si Concentration from

0 to 1000 ppm¶. Case 1 assumes that all U in UC and U2Si2MoC is 235U and Case 2 assumes that all U in UC and U2Si2MoC is 238U.

Additionally, based on the total number of atoms found in Step 1, the Mo concentration in the UMo matrix was also calculated as a function of Si concentration. The final Mo concentration in UMo matrix was first calculated in atomic percent by taking a ratio of the number of Mo atoms remaining in the UMo matrix after formation of U2Si2MoC and UC phases to the total number of all atoms in the UMo matrix. Here, we assume the only atoms in the matrix are U and Mo. Figure 6 and Figure 7 show change in Mo in atomic percent and weight percent, respectively, in the UMo matrix as a function of Si concentration up to 500 ppm. Concentration of Mo was first calculated in atomic percent, then converted to weight percent because Mo concentration related to UMo fuels is typically reported in weight percent, and the Mo weight percent in the UMo matrix varies for Case 1 in comparison to Case 2.

11

Figure 6. Mo Concentration (in at%) in UMo Matrix as a Function of Si Concentration for Both Cases 1 and 2.

12

Figure 7. Mo Concentration (in wt%) in UMo Matrix as a Function of Si Concentration for Cases 1 and 2.

Figure 6 and Figure 7 both illustrate the general trend that as Si concentration increases, the Mo concentration in the UMo matrix decreases. This observed trend is expected because as Si ppm increases, more Mo atoms are needed to form the U2Si2MoC phase, which means there are fewer Mo atoms in the UMo matrix. When atomic percent is converted to weight percent, the Mo concentration varies between Case 1 and Case 2 because the amount of 235U and 238U in the UMo matrix is different.

For Case 1, all the U in second phases (UC and U2Si2MoC) is assumed to be 235U, which has a lower molecular weight than 238U. As the Si content increases, Mo and 235U are needed to form U2Si2MoC in a ratio of 1:2 (number of Mo atoms to number of 235U atoms). Therefore, the weight of U in the matrix decreases, the entire weight of the matrix decreases, and the weight of Mo in the matrix decreases. This trend is observed for Case 2 as well; however Mo weight percent is lower than for Case 1 due to the fact that in Case 2 there is less 238U in the matrix (since all the U in second phases is assumed to be 238U), and thus the overall weight of the matrix is lower, and continues decreasing as Mo atoms are needed to form the Si-rich phase.

It is also noted that the Mo concentration in the UMo matrix calculated here will deviate from the expected 10 wt% (21.57 at%) with increasing Si concentration.

13

When there is no Si in the FA, the Mo concentration in the matrix is higher than the FA composition of 10 wt% (21.57 at%) Mo due to the presence of 1000 ppm C, which forms UC, thereby reducing the total U atoms in matrix and in turn increasing the atomic percentage of Mo.

Supplementary Information: The worksheet with the all calculations is provided in the accompanying Excel file, named “Si_balance_calculations_June2017.”

3.0 Future Work

The key motivation for this fundamental microstructure characterization work is that microstructure is linked to properties of the UMo fuel. At this time, better understanding of what and how microstructural features develop and how they are linked to properties (such as swelling) is important work to ultimately improve predictive capabilities linking properties to microstructure.

Future work will be focused on fundamental materials characterization of the UMo system in order to understand how the microstructure of this material system changes as a function of impurity element concentration (in particular, Si and C), and processing parameters such as time and temperature.

Specifically, we will investigate experimentally how the volume fraction of U2Si2MoC phase varies in the depleted uranium-molybdenum (DUMo) alloys as a function of homogenization temperature and time. We will investigate results of various homogenization times at 900°C and 1000°C. We have obtained evidence that with homogenization at 1000°C, the larger U2Si2MoC phase dissolves and thin plate-like precipitates of the same phase are formed. These observed microstructure changes also appeared to retard the time-temperature-transformation (TTT) kinetics during sub-eutectoid annealing treatments. We will investigate how the homogenization treatment temperature and time can be optimized to control the transformation extent in UMo alloys.

4.0 References

Burkes D, T Hartmann, R Prabhakaran, and J-F Jue. 2009. “Microstructural characteristics of DU–xMo alloys with x = 7–12 wt%.” Journal of Alloys and Compounds 479:140–147. Accessed July 24, 2017, at http://www.sciencedirect.com/science/article/pii/S0925838808022627.

Burkes D, R Prabhakaran, T Hartmann, J-F Jue, and F Rice. 2010. “Properties of DU-10 wt% Mo alloys subjected to various post-rolling heat treatments.” Nuclear Engineering and Design 240:1332–1339. Accessed July 24, 2017, at http://www.sciencedirect.com/science/article/pii/S0029549310001184.

Devaraj A, R Prabhakaran, EJ McGarrah, VV Joshi, SY Hu, and CA Lavender. 2016a. Theoretical Model for Volume Fraction of UC, 235U Enrichment, and Effective Density of Final U-10MO Alloy. PNNL SA 117284, Pacific Northwest National Laboratory, Richland, Washington. Accessed July 24, 2017, at http://www.pnnl.gov/main/publications/external/technical_reports/PNNL-SA-117284.pdf.

Devaraj A, VV Joshi, S Manandhar, CA Lavender, L Kovarik, S Jana, and BW Arey. 2016b. High Resolution Characterization of UMo Alloy Microstructure. PNNL-SA-26020, Pacific Northwest National Laboratory, Richland, Washington. Accessed July 24, 2017, at http://www.pnnl.gov/main/publications/external/technical_reports/PNNL-26020.pdf.

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Joshi V, E Nyberg, C Lavender, D Paxton, and D Burkes. 2015a. “Thermomechanical process optimization of U-10wt% Mo – Part 2: The effect of homogenization on the mechanical properties and microstructure.” Journal of Nuclear Materials 465:710–718. Accessed July 24, 2017, at http://www.sciencedirect.com/science/article/pii/S002231151530091X.

Joshi V, E Nyberg, C Lavender, D Paxton, H Garmestani, and D Burkes. 2015b. “Thermomechanical process optimization of U-10 wt% Mo – Part 1: High-temperature compressive properties and microstructure.” Journal of Nuclear Materials 465:805–813. DOI: 10.1016/j.jnucmat.2013.10.065. Accessed July 24, 2017, at http://www.sciencedirect.com/science/article/pii/S0022311513012312?via%3Dihub.

Jana S, A Devaraj, L Kovarik, B Arey, L Sweet, T Varga, C Lavender, and V Joshi. “Kinetics of cellular transformation and competing precipitation mechanisms during sub-eutectoid annealing of U10Mo alloys.” Journal of Alloys and Compounds Volume 723, 2017, Pages 757-771, ISSN 0925-8388, DOI: 10.1016/j.jallcom.2017.06.292. Accessed July 24, 2017, at http://www.sciencedirect.com/science/article/pii/S0925838817323009?via%3Dihub.

Nyberg EA, DE Burkes, VV Joshi, and CA Lavender. 2015. The Microstructure of Rolled Plates from Cast Billets of U-10Mo Alloys. PNNL-24160, Pacific Northwest National Laboratory, Richland, WA. Accessed July 24, 2017, at http://www.pnnl.gov/main/publications/external/technical_reports/PNNL-24160.pdf.